What is the integral of (1+ln(x))^2 ?

The integral of (1+ln(x))^2 is x+xln^2(x)+C

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integral of (1+ln(x))^2

\int (1 + ln (x))^{2} d x

x + x ln^{2} (x) + C

Solution steps

\int (1 + ln (x))^{2} d x

Apply Integration By Parts

: x (1 + ln (x))^{2} - \int 2 (1 + ln (x)) d x

= x (1 + ln (x))^{2} - \int 2 (1 + ln (x)) d x

\int 2 (1 + ln (x)) d x = 2 x ln (x)

= x (1 + ln (x))^{2} - 2 x ln (x)

Simplify

x (1 + ln (x))^{2} - 2 x ln (x) : x + x ln^{2} (x)

= x + x ln^{2} (x)

Add a constant to the solution

= x + x ln^{2} (x) + C

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What is the integral of (1+ln(x))^2 ?
The integral of (1+ln(x))^2 is x+xln^2(x)+C